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Home » In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is . What is the probability that he will knock down fewer than 2 hurdles?
In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is 5 / 6. What is the probability that he will knock down fewer than 2 hurdles?
CBSE | Class 12 | Maths | NCERT | Probability
In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is 5 / 6. What is the probability that he will knock down fewer than 2 hurdles?

Solution:

Assume that p represents the chance of a player clearing the hurdle and q represents the likelihood of a player knocking down the hurdle.

\therefore p=5 / 6 and q=1-5 / 6=1 / 6

Let us additionally assume that X is a random variable that indicates the number of times the player will knock down the hurdle throughout his or her turn.

\therefore By binomial distribution, P(X=x)={ }^{n} C_{x} p^{n-x} q^{x}

Hence, probability (players knocking down less than 2 hurdles) =P(X<2)

=\mathrm{P}(\mathrm{X}=0)+\mathrm{P}(\mathrm{X}=1)

={ }^{10} C_{0}(q)^{0}(p)^{10}+{ }^{10} C_{1}(q)(p)^{9}

=\left(\frac{5}{6}\right)^{10} \times\left[\frac{5}{6}+\frac{10}{6}\right]

=\frac{5}{2} \times\left(\frac{5}{6}\right)^{9}

=\frac{(5)^{10}}{2 \times(6)^{6}}

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